High interest rates will be around for quite a while despite Reagan administration predictions of much lower rates by the end of the year, the new president of the Virginia Bankers Association said last week.

"I am in complete accord with President Reagan's budget process and the proposed tax cuts," said Milton L. Drewer Jr., president of First American Bank of Virginia. "But we must face the realities that accompany the actions being taken by the Federal Reserve and the Depository Institutions Deregulation Committee.

"Some of the things that they have enacted recently and are suggesting for the future will virtually guarantee that high interest rates are here to stay." t

In remarks before the bankers' 88th annual convention, Drewer said interest rates won't be dropping soon because bankers must pay interest on NOW (negotiable order of withdrawal) accounts, checking accounts that previously paid no interest, and the phasing out of interest rate ceilings will force them to pay higher interest to customers.

"Add to this the proposed deregulation to allow us to compete with money market funds, and our total interest costs can only suggest that we must adjust to higher rates than we have historically experienced," Drewer said. "Reducing inflation cannot totally offset these costs, and we will have to find income to compensate for these expenses."

In addition, if interest costs rise by about 5 percent, then loan rates must increase by an equal amount for the bank to make a profit, Drewer said. "Higher rates, in some cases, variable rates will be a necessity."

"It sounds good" to eliminate interest ceilings so banks can pay small savers more on their money, "but this phase-out may also be the vehicle that will adversely affect their ability to borrow," he cautioned.

Drewer said a public relations campaign may be necessary to convince the public that bankers haven't conspired to keep interest rates high. The tight-money policies instituted by the Federal Reserve Board to keep inflation under control are part of the problem, he said.

"We must all take a closer look at this permanent institution of high interest rates that is being perpetuated, because we the bankers may be viewed as being the cause of high rates when, in fact, we are not," Drewer said.

The Reagan administration has predicted that its economic recovery plan will lead to lower interest rates. On Monday, Treasury Secretary Donald T. Regan said high interest rates are a temporary phenomenon that will pass, and many economists have been saying for weeks that interest rates will come down.

This year the lowest prime rate was 17 percent, about the first of April. Since then it has risen steadily and remains at about 20 percent.

Outgoing Virginia Bankers Association president C. Coleman McGehee has noted other emerging problems for banks. He said the biggest challenge to the commercial banking industry today is competition from large, nonbank financial conglomerates such as American Express Co.

Other challenges include stemming the outflow of assets from banks, controlling the growth of foreign ownership of U.S. banks and reducing government restrictions on banks, McGehee said last week in an address to the association's 88th annual convention.

"We bankers are natural competitors," said McGehee, chairman of First & Merchants Corp., one of the state's largest bank-holding companies. But the real competition is outside of banks, within large, nonbank financial conglomerates that can offer check-writing privileges and credit cards but are not restricted by government requirements to set aside reserve funds on a portion of their business volume, McGehee said.Conglomerates also can serve customers across state lines, but banks cannot, he noted.

"Investment money market funds on deposit with these firms continue to grow and now have total assets in excess of $130 billion, versus $70 billion a year ago," McGehee said. "Banks must be unshackled from the current restrictive regulations and allowed to compete head-on in a free market environment."

Banks should be allowed to issue money market funds similar to those offered by nonbank financial institutions and they should be able to underwrite municipal revenue bonds, McGehee said. In addition, savings and loans "can't insist on interest-rate-differentials" they have enjoyed to attract funds for mortgage lending, McGehee declared.

Commercial banks are losing their market share of total financial assets, he pointed out.

"In 1948 the commercial banking industry accounted for 81 percent of the assets of the nation's financial institutions," McGehee said. "In 1980 this figure had shrunk to 56 percent and it is still falling."

McGehee added that bank ownership by foreigners is increasing.

"Only two U.S. banks remain among the top 10 worldwide, as compared to five a decade ago," he said.

Another challenge the banks face is how to promote good working relations between men and the growing ranks of women in bank management, said Jane McGavock Smith, president of the National Association of Bank Women, Inc. Some women managers and men don't know how to treat each other in a professional setting, Smith said. Also, many women encounter conflicts between banking careers and their families, she told the bankers.